Solve the equation 3 x+4 x=0 for all in the interval

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Solve the equation

3\sin x+4\cos x=0

for all

x

in the interval

[0,2\pi)

. (a) Transform the given equation into the form

\tan x=k

and state the value of

k

. (b) Using appropriate quadrant considerations, determine all solutions of

\tan x=k

that lie in

[0,2\pi)

. (c) Verify that each solution obtained satisfies the original equation.